This is an older brick and siding home with a full basement. It has a heat pump and our electric rates were just raised 31%! Needless to say we are trying to figure out how to save money. My question is, if I close the vents in the basement so that part of the house is not heated, we only use the laundry room, will I be able to save money, and will it hurt the heat pump?

Probably not, but provide a little more info... how many vents do you have (total), and how many serve the basement?